Analysis of the MHD Nanofluid boundary layer flow over a rotating disk with a constant velocity in the presence of hall current and non-linear thermal radiation has been covered in this work. The variation of viscosity and thermal conductivity of the fluid due to temperature and nanoparticles concentration and size is considered. The problem described by a system of P.D.E that converted to a system of ordinary differential equations by the similarity transformation technique, the obtained system solved analytically using Optimal Homotopy Asymptotic Method (OHAM) with association of mathematica program. The velocity profiles and temperature profiles of the boundary layer over the disk are plotted and investigated in details. Moreover, the surface shear stress, rate of heat transfer explained in details.

In this paper, the effect of convective boundary conditions, heat generation, Brownian motion, and thermophoresis on heat transfer characteristics of a moving cylinder embedded into cooling medium consists of water with nanoparticles are studied. The governing boundary-layer equations transformed to ODE using similarity transformation method and then solved analytically using optimal homotopy asymptotic method for the general case. The velocity, temperature, and concentration profiles within the boundary-layer plotted and discussed in details for various values of the different parameters. Moreover, the effect of boundary-layer behavior on the surface shear stress, rate of heat and mass transfer investigated.